6.4 Illustration of the methodology by examples
6.4.1 Energy consumption calculation by selective laser sintering
pl,
platform m
E E
(6.33) where ηm is the efficiency of the motor.
6.3.5 Miscellaneous energy consumptions
Apart from the energy consumption sources mentioned in Sections 6.3.1–6.3.4, energy is also consumed by the computer, workstation and some energy are also lost in the form of heat and machine error (Song and Telenko 2017, Yosofi et al. 2018). The energy consumed by miscellaneous sources (Emisc) is approximated as 5% of the total energy consumed by all other sources, i.e.,
0.05 .
misc melting baseplate platform extrusion
E E E E E (6.34)
Table 6.2 Parameters for energy consumed by the laser and heater system
Parameters Value Basis
Power rating of the laser (W) 30 (SLS SPEC 2017), own judgement (based on literature review)
Scan velocity of the laser (mm/s) 700 (Pham and Wang 2000), own judgement
Laser beam diameter (mm) 0.6 (Zhang and Bernard 2013) Power of infrared heater (W) 1000 (Deziel 2018)
Efficiency of infrared/resistive heater
0.9 Own judgement
Specific heat of powder (kJ/kgK) 2.5 (Franco and Romoli 2012)
Tfinal of powder (°C) 185 (Franco and Romoli 2012)
Tinitial of powder (°C) 20 (Franco and Romoli 2012)
The next step involves the energy estimation by the roller for spreading and levelling the powder. The kinematic behaviour of the roller is illustrated in Figure 6.1. The roller travels to-and-fro across the platform based on the number of layers present in the part. For each travel, the roller consumes energy. The procedure to estimate the time taken by the roller to travel from one end of the platform to the other is explained in Chapter 3.
The data used for estimating roller energy is given in Table 6.3.
Table 6.3 Parameters for estimating the roller energy
Parameter Value Basis
Distance travelled by roller (mm) 506 (SLS SPEC 2017), own judgement Velocity of roller (mm/s) 700 (Pham and Wang 2000), own judgement Acceleration of the roller (mm/s2) 20000 (CADEM 2017)
Time, t1–t2 (s) 0.69 By calculation
Mass of roller (kg) 5 Own judgement
Diameter of powder (μm) 100 (Duraform n.d.) Radius of the roller (mm) 50 (Haeri et al. 2016) Force required by roller (N) 326.94 (Nan et al. 2020)
Efficiency of the motor 0.75 Own judgement considering part load operation
Lastly, the energy consumed by the moving pistons is estimated. The total vertical distance travelled by the piston of the build platform is equal to the height of the part. For the build piston, an additional 20% increase is included in the mass of the piston to consider the mass of the powder deposited. The parameters for estimating the energy consumed by piston is given in Table 6.4. The piston lowers down according to the prescribed layer thickness and the number of layers present in the part. An additional 5% increase is included
in the number of times the piston is lowered. However, the total distance travelled by piston of the powder delivery piston is much more than the piston of the build platform. The powder delivery piston feeds the powder to the height equal to the radius of roller, i.e., 50 mm. This process is repeated for every number of layers of the part. Also, the piston has to travel to the bottom frequently for complete filling of the feedstock with powder. This is done by an external delivery source. Considering these effects, an additional increase of 50% of the mass of the piston is also included. Hence, the energy of the piston for powder delivery is much more than the piston of the build platform. Finally, based on Eqs. (6.32) and (6.33), the energy consumed by the pistons
Table 6.4 Parameters for estimating the energy consumed by the pistons
Parameters Value Basis
Mass of the platform (kg) 10 Own judgement
Velocity of the platform (mm/s) 700 Own judgement
Efficiency of the motor 0.75 Own judgement considering part load operation
Table 6.5 Energy consumption by different sources for part A and part B
Energy components Value
Part A Part B
Energy consumed by laser system (kJ) 45.04 2.34
Energy consumed by infrared heater (kJ) 6954.67 4072.27 Energy consumed by resistive heater(kJ) 570.26 692.46 Energy consumed by the roller in spreading the powder (kJ) 80.19 144.95 Energy consumed by the piston by build platform (kJ) 0.78 0.94 Energy consumed by the piston for powder delivery (kJ) 4.58 4.89 Miscellaneous energy consumption (computer, losses) 382.78 245.89 Total energy consumption of the part (kJ) 8038.29 5163.74 Total energy consumption of the part (kWhr) 2.23 1.43 Total energy consumption per unit mass of the part (kJ/kg) 51756.42 639868.65 Total energy consumption per unit build time (kJ/hr) 4623.25 5072.1 is estimated. The energy consumed by every component for manufacturing part A and part B considering a single quantity is listed in Table 6.5. As evident from the last two rows of the table, mass of the part and build time may give some indication about the energy consumption, but it also depends on the part complexity.
6.4.1.1 Estimation of energy considering multiple quantities of a part in the machine chamber
The energy required by the laser and the infrared heater varies with the number of quantities manufactured in the machine chamber. However, the energy consumed by the resistive heater, roller and the pistons is independent of the number of quantities manufactured in the machine chamber. Hence, if more than one quantity of a part is manufactured, the overall unit energy requirement is less as the energy is reduced amongst the resistive heater, roller and pistons. As per the size of part A, only two quantities can be manufactured at a single setting of the machine chamber. In such a case, the total consumed energy is estimated as 12119.91 kJ whereas unit energy consumption is 6059.96 kJ. Hence, in manufacturing two quantities of part A, energy consumption is reduced by approximately 25% for a part. On the other hand, considering the smaller sized part B, a maximum of eighteen quantities can be manufactured in a single setting. This is also referred to as full utilization of the machine. The energy consumed for manufacturing a single quantity of part B is 5163.74 kJ whereas the unit energy consumed for eighteen quantities is 1004.67 kJ reducing the energy consumption by 81%. The variation of energy with the quantities of part B is shown in Figure 6.3.
Figure 6.3 Variation of energy consumption with quantities of part B
6.4.1.2 Implementation of fuzzy arithmetic in energy consumption calculation of SLS This section considers uncertain parameters as fuzzy and the energy consumption in SLS is obtained as a fuzzy number. The fuzzy parameters are expressed as low (l), most likely (m) and high (h) estimates in Table 6.6. In the estimation of energy consumed by the roller, the lower limit of roller force is assumed to deviate by 20% whereas the upper limit by 10%
than the most likely estimate. The height of the heap of powder accumulated in front of the roller is assumed to vary by 10% and 20% of the radius of the roller for the lower and upper estimates, respectively. Also, the lower and upper limit of the size of the roller is considered to be 500 and 1000 times that of the size of the powder. In the estimation of energy consumed by the pistons for build platform, the lower and upper limits of mass of the piston are additionally increased by 10% and 30% of the actual mass of the piston, respectively.
However, for the piston of the powder delivery platform, the lower and upper limits are increased by 30% and 70%, respectively. This piston has to accumulate relatively more mass of the powder that is continuously fed by the feedstock.
Table 6.6 Fuzzy parameters considered for estimation of energy consumption in SLS
Parameter (l, m, h)
Power rating of the laser (W) (20, 30, 50) Scan velocity of the laser (mm/s) (500, 700, 1000) Power of infrared heater (W) (800, 1000, 1200) Efficiency of infrared/resistive heater (0.8, 0.9. 0.95)
Diameter of the roller (mm) (50, 75, 100)
Mass of roller (kg) (4.5, 5, 5.5)
Force required by roller (N) (313.86, 435.92, 527.46)
Layer thickness (mm) (0.12, 0.15, 0.21)
Table 6.7 shows the unit energy consumption of the parts considering a single quantity and full utilization of the machine chamber, i.e., two and eighteen quantities of part A and part B, respectively. The energy as a fuzzy number is obtained by applying the procedure mentioned in Section 3.3. The variation of energy as a fuzzy number with different membership grades is shown in Figure 6.4.
Table 6.7 Unit energy consumption as a fuzzy number considering a single part and full utilization of the machine
Quantities in the machine chamber
Unit energy consumption (kJ) Low
estimate (l)
Most likely estimate (m)
High
estimate (h)
Part A 1 4930.94 8038.29 14970.4
2 3534.51 6059.96 11776.59
Part B 1 4160.02 5163.74 7637.45
18 714.87 1004.67 1659.19
(a)
(b)
Figure 6.4 Representation of energy consumption as a fuzzy number for parts produced by SLS: (a) Considering a single quantity, (b) considering full utilization of the machine chamber (two and eighteen quantities of part A and part B, respectively)